一类非线性双曲型方程Goursat问题的奇摄动

本文研究一类非线性奇摄动问题：在适当的假设下，讨论了相应问题解的存在性和唯一性，构造了其解的形式渐近展开式，并证明了它的一致有效性。

A Class of Singular Perturbation for the Goursat Problems of Nonlinear Hyperbolic Equation

Consider the nonlinear singularly perturbed problem :where e is a positive parameter and under other suitable conditions,we can prove that there exists a unique solution w(x,y,e) ,and the uniformly valid asymptotic expansion holds:where is a m-approximation of the outer solution and is a corrective term.